The 29-year-old Frenchman raced with the Faenza based team last year, but so far only the Swiss rookie Sebastien Buemi has been confirmed for the forthcoming season.
2009 would therefore be Bourdais' second season in formula one, following his mixed debut, when he finished the championship with just 4 points compared with his Red Bull-bound teammate Sebastian Vettel's 35.
It is reported by the Swiss magazine Speedweek, with close links to the team's owner Red Bull, selected Bourdais over the other candidate for the seat, Takuma Sato.
The French website sport24.com speculated that Sato's expected personal sponsorship may have dwindled as the Japanese recession worsens.
Bourdais' manager Nicolas Todt would not confirm the news but insisted that "we are always in negotiations".
Moreover, the official website of the Ferrari-powered team is now showing Bourdais and Buemi as the drivers in the 'team' section.